Hi pads69
This one is quite a puzzle. I am a bit surprised that you hear much white noise with DAB. As it is a digital system, reception tends to flip from very good to non existent as the signal to noise ratio drops, with only a pretty narrow window of burbly broken up reception between the two conditions. FM on the other hand will exhibit white noise over a larger window between good and no reception. Clearly, the audio stages are OK as you can play the ipod successfully. If it affects more than one radio, it suggests the cause is external to the radio but associated with the engine or something only powered when the ignition is on. When you turn off the engine, some engine management systems carry on being powered up for a minute or two but do eventually go to sleep. Habitation electronics might be on most of the time, though some functions are normally disabled once the engine is running.
Two things spring to mind:
Possibility 1: Part of the engine management system is radiating a high level of radio noise (which it shouldn't) which is being picked up by the radio antennas. The gradual rather than sudden onset and the time delay to me suggest that this effect is only happening once something has warmed up, and if it takes 20 minutes that "something" has quite a high thermal mass. I can only suggest that you find a small battery powered FM portable radio and telescope the antenna down to just one section and tune it to a weak-ish station. Moving it around the engine bay with the engine hot and running might help you to physically pinpoint the source of maximum radiated noise, though be aware that cable looms are a favourite for radiation of interference generated by items they connect to.
Possibility 2: Something in the battery charging circuit starts generating more noise as the charge state alters in the batteries. You would normally expect that to stop immediately the engine stops and the alternator therefore ceases charging. However, a modern setup with a Battery to Battery (B2B) converter may carry on after the engine has stopped, it all depends on the design of the habitation electronics package which is often bought in by the MH converter from a 3rd party supplier. It would be worth experimenting with the settings of the habitation battery controller (including shutting it right down) to see if it makes a difference. If you do indeed have a B2B converter, by design it is very rapidly switching tens of amps of current which is a recipe for generating high levels of radio noise. Radiation will take place by the associated wiring acting as an antenna, and it then only has to travel a metre or two before it gets into the radio antennas. Although the B2B will undoubtedly have some internal filtering, this may be insufficient. Try "sniffing" around the B2B and its wiring with the portable FM radio. If the B2B is the culprit, it may help to place several ferrite suppressor toroid cores over the input and output DC cables (these cores are split to allow them to be clipped over without disconnecting the wires). Their effect is to make the cables much less efficient as radiating antenna whilst not affecting them at DC. You might have seen something similar as the "lump" on the wires of phone chargers etc.
I don't know if there is a forum for Autosleepers owners, but if this is a design problem rather than sometjing with a fault one might expect other owners to have suffered the same thing.
As a final thought, it's just possible that the noise is being conducted along any of the wiring into the radio, rather than being received "off air" by the antennas. Although such noise should be rejected by built filtering within the radio, I guess if its at a really high level it could still break through. However it seems very unlikely that two radios of different design would be affected in the same way. In this situation the portable FM radio mentioned above will be unaffected as it has its own isolated batteries so there is no conduction path. Conducted noise like this is fairly straightforward to fix by means of extra filtering next to the radio.